Principles and Practice of Pharmaceutical Medicine

In this equation,kdis the apparent first-order degra-
dation rate constant (also calledkout). This constant
can be obtained experimentally from the slope of a
ln(P) versus time plot, after administration of a
synthesis-blocking dose of coumarin anticoagulant
(Nagashimaet al., 1969; Pitsuiet al., 1993).P 0 is
the baseline value of the prothrombin time,Cw(s)is
the concentration of (S)-warfarin and IC50sis the
concentration of warfarin at 50% of maximal
blocking effect. It was also possible to estimate
the half-life of the apparent first-order degradation.
An alternative model, including a lag-time to
allow for distributional effects embedded in the
observed time delay of the onset of the effect
after warfarin administration, was published by
Pitsuiet al. (1993). Setting the baseline value of
clotting factor activity in the absence of warfarin
(P 0 ) to a fixed mean of three predose measure-
ments, the program can estimate that parameter.
The model equations are as follows:

d PCA

dt

¼

Kin

IðCwðsÞÞ

kdP

whereI(CwðsÞ) is the inhibition function of warfarin
(see next equation). It is appropriate to substitute
KinwithkdP 0. Inhibition of synthesis (rate in)
has an impact on the peak (trough) level rather than
the time to the peak. This is similar to a constant

rate of drug infusion into a one-compartment sys-

tem. The time to steady state is only governed by

the elimination rate constant and not the rate of

infusion. At steady state:

dR

dt

¼

Kin

IðCwðsÞÞ

koutP¼ 0

If the baseline condition for PCAwith no inhibition

of drug is:

PCA¼P 0

then the steady-state condition for the pharmaco-

logical response (PCAss) with drug present

becomes:

PCAss¼

P 0

IðCÞ

¼P 0

1

1 þ

CwðsÞ

IC50s

n

and whereI(CwðsÞ) is a function ofCw(s),nand

IC50s, then:

IðCwðsÞÞ¼ 1 þ

CwðsÞ

IC50s

n

As stated before, the intensity of a pharmacologi-

cal response may not be due to a direct effect of the

drug on the receptor. Rather, it may be the net

result of several processes only one of which is

influenced by the drug. The process that is influ-

enced by the drug must be identified and an

attempt be made to relate plasma drug concentra-

tion to changes in that process. Warfarin provides a

good example of this, as the anticoagulant (hypo-

thrombinemic) effect is an inhibition of the synth-

esis of certain vitamin K-dependent clotting

factors.

Initial parameter estimates were obtained from

the PCAversus time data. The baseline value (120 s)

was obtained from the intercept on the effect axis.

This value is the ratioKin/kd. From the intercept and

slope,Kinwas calculated tobe 3.5 s h
^1 .Theplasma

concentration at the time of the trough of the effect

corresponded approximately with the EC 50 value.

Thus, IC 50 ¼0.35 mg 1
^1 ,kd¼ 0 : 3 h
^1 ;n¼ 3 : 5 ;

0

20

40

60

80

100

120

140

24 48 72 98 120 144

PCA

Time (days)

Figure 8.6 Observed PCA time course following the
administration of an intravenous bolus dose of warfarin

94 CH8 PHASE I: THE FIRST OPPORTUNITY FOR EXTRAPOLATION FROM ANIMAL DATA